What is the integral of (x+1)/(sqrt(x^2+2x+5)) ?

The integral of (x+1)/(sqrt(x^2+2x+5)) is sqrt(x^2+2x+5)+C

Popular >

integral of (x+1)/(sqrt(x^2+2x+5))

\int \frac{x + 1}{x ^{2} + 2 x + 5} d x

x^{2} + 2 x + 5 + C

Solution steps

\int \frac{x + 1}{x ^{2} + 2 x + 5} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = x^{2} + 2 x + 5

= \frac{1}{2} \cdot 2 (x^{2} + 2 x + 5)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (x^{2} + 2 x + 5)^{\frac{1}{2}} : x^{2} + 2 x + 5

= x^{2} + 2 x + 5

Add a constant to the solution

= x^{2} + 2 x + 5 + C

\int 2 x^{2} 4 x^{3} - 7 d x

\int sin (5 t) sec^{2} (cos (5 t)) d t

\int \frac{- 6}{x ^{2}} d x

\int e^{(\frac{x}{3})^{3}} x^{2} d x

\int \frac{- 2 x ^{2}}{9 - x ^{2}} d x

What is the integral of (x+1)/(sqrt(x^2+2x+5)) ?
The integral of (x+1)/(sqrt(x^2+2x+5)) is sqrt(x^2+2x+5)+C